To answer the actual question, vegetable probly became "vechtable" the first time it was pronounced in a hurry.
There are four possible syllables; in order, with ruffli funnedik spelling,
- VEH (primary stress)
- juh (unstressed, reduced vowel)
- tuh (unstressed, reduced vowel)
- bull (secondary stress)
The first syllable is stressed, followed by two unstressed syllables. Those two syllables (2-3) normally coalesce into one syllable at speech rate (in American English, at least), like will not into won't, or I will into I'll. Except the spelling doesn't show it, because English spelling doesn't show anything much.
They do this by dropping the unstressed schwa (uh) in (2) between J and T, putting those two stops into contact. Now J is really D plus ZH, and they're both voiced consonants. But T is voiceless. And they form a consonant cluster after the vowel between them gets deleted -- that is, they hafta be pronounced together, in a bunch.
There's a very strong tendency in all languages where voicing and consonant clusters occur, including English, for consonant clusters to be either
- composed of all voiceless consonants: loft, spy, laps, gets
or
- composed of all voiced consonants: luhvz, dzhordzh
So what happens is that J and T hafta be all voiced or all voiceless. And in English it's the last consonant in the cluster that decides the voicing, when a cluster is formed this way. That consonant is T and it's voiceless, so J is devoiced to CH (T plus SH) to match it. And you wind up with VECHtuhbull.
The process is completely automatic, like changing the vowel nucleus of the vowel in fife, but not the one in five, because fife ends in a voiceless sound. These are not things that happen to letters, by the way; they are are parts of the muscle and nerve patterns that inform the ways we pronounce the actual words. This is Phonetics, in particular the phonetics of English consonant clusters.